Find the HCF of each of the following by common division method.
24, 96, 108

Answer

To find the HCF (Highest Common Factor) of the numbers 24, 96, and 108 using the common division method, follow these steps:

### Step 1: Arrange the Numbers
Identify the numbers given in the question:
- 24
- 96
- 108

### Step 2: Start with the Smallest Number
Begin with the smallest number, which is 24, and divide the other numbers by it.

### Step 3: Divide 96 by 24
Perform the division:
- \( 96 \div 24 = 4 \) (exact division, remainder is 0)

### Step 4: Divide 108 by 24
Now, divide 108 by 24:
- \( 108 \div 24 \)
- 24 goes into 108 four times (4 x 24 = 96), leaving a remainder:
- \( 108 - 96 = 12 \)

### Step 5: Now, Use the Remainder
Now we will use the remainder (12) and divide it into the previous divisor (24):
- \( 24 \div 12 = 2 \) (exact division, remainder is 0)

### Step 6: Check the Last Remainder
Now, we need to check if 12 can divide 108:
- \( 108 \div 12 = 9 \) (exact division, remainder is 0)

### Step 7: Conclusion
Since we have reached a point where the last remainder is 0, the HCF of the numbers 24, 96, and 108 is the last divisor we used, which is 12.

Thus, the HCF of 24, 96, and 108 is **12**.

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